calculate the values of 2. f * x ^ 2 + y ^ 2 = 5/8 * and * 4/3 * xy = 1/4 (a) (x + y) (b) (x-y) (c) (x^2-y^2)
Answers
Answer:
(a) 1
(b) 1/2
(c) 1/2
Step-by-step explanation:
[tex]x^2 + y^2 = 5/8 (1)\\\frac{4}{3}xy = \frac{1}{4} (2)\\\\\textrm {From (2) by multiplying both sides by 3/4 we get}\\\\xy = \frac{3}{16} (3)\\\textrm{We know that } (x + y)^2 = x^2 + 2xy + y^2 \\\textrm{Adding 2xy to the LHS and RHS of equation 1 gisues us }\\x^2 + y^2 + 2xy = \frac{5}{8} + 2 * \frac{3}{16} = \frac{5}{8} + \frac{3}{8} = \frac{8}{8} = 1[/tex]
[tex](x + y)^2 = 1 == > x+y = \sqrt{1} = 1\\\\(x - y)^2 = x^2 -2xy + y^2\\\\\textrm{Subtracting 2xy from both sides of Equation 1}\\x^2 + y^2 - 2xy = \frac{5}{8} - 2*\frac{3}{16} = \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \\x-y = \sqrt{\frac{1}{4}} = \frac{1}{2}\\\\x^2 - y^2 = (x+y)(x-y) = 1 . \frac{1}{2} = \frac{1}{2}[/tex]
Related Questions
how do i find the slope of the line containing ordered paid? A(2,-5), B(-2,6)
Answers
The slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the given containing ordered paid A(2,-5) and B(-2,6) is:
Slope = 6+5/-2-2 = 11/-4
Hence, the slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.
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Determine the equation of the parabola shown in the diagram in vertex form. (check picture below)
Answers
The equation of the parabola is y - 1 = (2/3) * (x - 3)².
What is equation of the parabola ?The general equation of a parabola is: y-k = a(x-h)²
(h, k) - Coordinates of the vertex.
a - Vertex constant
Here:
(h, k) = (3, 1) and (x, y) = (0, 7).
So,
7 - 1 = C · (0 - 3)²
6 = 9 · C
C = 2/3
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Find all the possible values of tan^-1 1
Answers
The possible values of tan^-1(1) are (3π + 4n)/4
How to determine the possible values?The expression is given as:
tan^-1(1)
To determine the possible values, we plot the graphs of
y = tan(x) and y = 1
From the graph, we have the following values
tan^-1(1) = (3π + 4n)/4 when n = ±{0,1,2....}
Hence, the possible values of tan^-1(1) are (3π + 4n)/4
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what are the possible numbers of positive, negative, and complex zeros of f(x)=-3x^4+5x^3-x^2+8x+4
Answers
Answer:
There could be 0, 2, or 4 complex solutions
Step-by-step explanation:
The Fundamental Theorem of Algebra states that any polynomial with n degree will have n solutions So since the degree of the polynomial you provided has a degree of 4, that means there are 4 possible solutions. This question specifically asks for complex zeroes. Complex zeroes come in conjugate pairs, so that means if you have one complex zero, there is another complex zero which is it's conjugate. For this reason, there can only be an even number of complex zeroes. And since there's 4 possible solutions, There could be 0, 2, or 4 complex solutions
What is the measure of z?
Z
X
y
4
9
z = [ ? ]VI
Answers
Answer:
z= [ 5] VI
that is my answer
At a weather station in the Artic the temperature was recorded as -23° C.
Two hours later it had fallen by 11° C.
(i) What was the new temperature?
()Four hours after the first readings the temperature was -45° C.
By how much had the temperature fallen in four hours.
Answers
Answer:
(i) -34° C.
(ii) The temperature had fallen by 11° C.
Step-by-step explanation:
(i) As it's a negative number its like we are adding it so 23 + 11 = 34 and as it is a negative number it would be -23 - 11 = -34 which makes it -34° C.
(ii) We know that the temperature now is -45° C, we need to find out how much the temperature had fallen in the 4 hours which had passed. So what we do is essentially add it considering its a negative number so we add -34 by 11 which equals -45. We do this so we can find out how much the temperature had dropped within the 4 hours and as we know that we needed to add 11 to the previous temperature (-34° C) it means that the temperature has dropped by 11° C.
Calculate: 6666666x666666/1+2+3+4+5+6+5+4+3+2+1- 777777x777777/1+2+3+4+5+6+7+6+5+4+3+2+1
Answers
Answer: 3.8395025e+12
Lol
3839502493910
Step-by-step explanation:
you will multiple the 6 and the 7 digits and the other digits
Use slope-intercept form to write the equation of a line that has a slope of −3 and passes through the point (1, −5).
y=
x=
m=
Answers
Answer:
y=-3x-2
Step-by-step explanation:
The slope-intercept form is y=mx+b
where m is slope and b is y-intercept.
Substitute m=-3 and point (x,y)=(1,-5) into the equation:
-5=-3(1)+b
-5=-3+b
b=-5-(-3)=-5+3=-2
Therefore, the required equation:
y=-3x-2
isabella and aiden get a reward of $119 in the ratio of 4 3, what fraction of the total reward does isabella get
Answers
Using proportions, considering the given ratio, Isabella gets [tex]\frac{4}{7}[/tex] of the total reward.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The ratio of Isabella and Aiden is 4:3, which means that out of 4 + 3 = 7 items, Isabella gets 4 and Aiden gets 3, hence the fraction is given by:
[tex]\frac{4}{7}[/tex].
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For each of the following a) identify the inverse function needed to solve for the indicated angle and b) solve for the angle (round to the nearest tenth of a degree).
Answers
The angle is the cosine inverse function because base over hypotenuse. Then the angle will be 37°.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The triangle with base of 4 units and hypotenuse of 5 units.
We know that the angle is given by the cosine inverse function because base over hypotenuse. Then we have
⇒ cos⁻¹ (4/5)
Then the angle will be
⇒ 36.869 ≈ 37°
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Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible?.
Answers
Suppose that a probability is approximated to be zero based on empirical results, this does not mean that the event is impossible.
What is probability?The likelihood that an event will occur is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
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How many x-intercepts does the graph of y=2x^2-4x+2 have?
A.0
B.1
C.2
Answers
Answer:
B. 1
Step-by-step explanation:
Please see attachment.
Hope this helps!
If not, I am sorry.
A number line goes from negative 5 to positive 5. Point D is at negative 4 and point E is at positive 5. A line is drawn from point D to point E.
What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio?
Negative one-eleventh
One-eleventh
Two-fifteenths
Fifteen-halves
Answers
Directed numbers are numbers that have either a positive or negative sign, which can be shown on a number line. Therefore, point F is Fifteen-halves of line segment DE.
A number line is a system that can show the positions of positive or negative numbers. It has its ends ranging from negative infinity to positive infinity. Thus any directed number can be located on the line.
Directed numbers are numbers with either a negative or positive sign, which shows their direction with respect to the number line.
In the given question, the distance between points D and E is 9 units. So that dividing 9 units in the ratio of 5 to 6, we have;
[tex]\frac{5}{6}[/tex] x 9 = [tex]\frac{45}{6}[/tex]
= [tex]\frac{15}{2}[/tex]
Therefore, the location of point F, which partitions the directed line segment from d to E into a 5:6 ratio is [tex]\frac{15}{2}[/tex]. Thus the answer is Fifteen-halves.
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Answer:
1/11
Step-by-step explanation:
Got it right on assignment
Which of the following expressions represents the given algebraic tiles
Answers
The expression that represents the given algebraic tiles is 2x² + 6x + 6
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The expression for the given algebraic tiles is:
Total = x + x + x + 1 + 1 + 1 + x² + x + x + x + 1 + 1 + 1 + x² = 2x² + 6x + 6
The expression that represents the given algebraic tiles is 2x² + 6x + 6
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According to the data in the figure, find the value of x and y.
Answers
Answer:
This is a educated guess, but x is 80 and y is 100.
Step-by-step explanation:
My logic here is that the triangles are the same because of all the congruent lines and stuff. But from there, you know that both the right and the left side are 40 degrees. You know the total degree of a triangle is 180 so 180 - 40 - 40 is 100. So the final angle is 100. If you look at x, its on the outside, but on a line. If you can imagine a circle, its half, so its a 180 degrees total. Then its 180 = x + 100. So x is 80. And then by that same logic its y = 100.
What is the decimal expansion of the following fraction? 1/2
Answers
Answer:
the answer is 0.5
Step-by-step explanation:
The answer for this is 0.5
if you apply to college as a freshman in 2023, and they accept you, when you start going to college?
Answers
Answer: Likely May through August 2023
Step-by-step explanation: It really depends on the college.
Simplify : i) (〖6x〗^2+x-7)/(12x^2+14x)
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of the given expression can be done as,
[tex]\dfrac{(6x)^2+x-7}{12x^2+14x}\\\\\\=\dfrac{36x^2+x-7}{12x^2+14x}\\\\\\=\dfrac{(6x)^2+x-7}{2(6x^2+7x)}[/tex]
Hence, the simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].
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Find the area of a circle with radius, r = 5.64m.
Give your answer rounded to 2 DP.
r
The diagram is not drawn to scale.
Answers
Answer:
99.93 [tex]m^{2}[/tex]
Step-by-step explanation:
1. The area of a circle is defined by the equation: A = [tex]\pi r^{2}[/tex]
2. We can plug in the radius and solve the equation: A = [tex]\pi *5.64^{2}[/tex]
3. A = π * 31.8096
4. A = 99.932
5. A = 99.93
Please help me. Due today. Please show work so I can get it correct!!!!
Answers
Based on the inscribed angle theorem, the value of x is: 126°.
What is the Inscribed Angle Theorem?The inscribed angle theorem states that, the measure of inscribed angle (63 degrees) equals half of the measure of central angle (x).
Thus, we would have:
63 = 1/2(x)
2(63) = x
126 = x
x = 126°
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The minimun point on the graph of the equation y=f(x) is -1,-3. What is the minimum point on the graphof the equation y=f(x-5)
Answers
The minimum point on the graph of the equation y=f(x-5) is (-6, -3)
How to determine the minimum?The initial minimum is given as:
(-1, -3)
The transformation y = f(x - 5) means that:
(x, y) = (x - 5, y)
So, we have:
(x, y) = (-1 - 5, -3)
Evaluate
(x, y) = (-6, -3)
Hence, the minimum point on the graph of the equation y=f(x-5) is (-6, -3)
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Sam opened a savings account with $400. He earns $1,640 a
month at his job and will deposit 3% of his monthly pay every
month into his new savings account. Assuming he doesn't
withdraw money from his savings account, which equation shows
the balance y of his savings account x months after he opened it?
y = 12x + 400
y = 400x + 1640
y = 49.2x + 400
y = 0.03x + 400
Answers
Answer:
y = 49.2x+400
Step-by-step explanation:
He deposits 3% of his monthly pay = 0.03*1640 = $49.2 every month = 49.2x
He put $400 when he opened the account so that needs to be added in = 49.2x+400
Can someone help.
Triangle not drawn to scale
Given: m = 53°, a = 18, and c = 14. Find me to the
nearest whole number.
Answers
Answer:
m∠C = 38° (nearest whole number).
Step-by-step explanation:
To find the missing angle, use the Sine Rule.
Sine Rule (for angles)
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
where:
A, B and C are the anglesa, b and c are the sides opposite the anglesGiven:
A = 53°a = 18c = 14To find m∠C, substitute the given values into the formula and solve for C:
[tex]\implies \sf \dfrac{\sin 53^{\circ}}{18}=\dfrac{\sin C}{14}[/tex]
[tex]\implies \sf \sin C= \dfrac{14 \sin 53^{\circ}}{18}[/tex]
[tex]\implies \sf C= \sin^{-1} \left( \dfrac{14 \sin 53^{\circ}}{18}\right)[/tex]
[tex]\implies \sf C= 38.40096301...^{\circ}[/tex]
Therefore, m∠C = 38° (nearest whole number).
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im not sure how to solve this question ???
Answers
Answer:
Part A) B
Part B) D
Step-by-step explanation:
Given:Total sweets = 10
Red = 4
Green = 2
Yellow = 3
Purple = 1
A = 2/10 = 1/5
B = 3/10
C = 4/10 = 2/5
D = 1
Solution:Part A)Yellow sweets = 3
Total = 10
Probability = yellow/total
Probability = 3/10Hence, B shows the probability of showing a yellow sweet.
Part B)Sweets that are not orange = 10 (All sweets are not orange)
Total = 10
Probability = sweets that are not orange / total
Probability = 10 / 10
Probability = 1Hence, D shows the probability of choosing a sweet that is not orange.
[tex]\rule[225]{225}{2}[/tex]
find the area of the following figure..
Answers
Answer:
456 [tex]cm^{2}[/tex]
Step-by-step explanation:
Find the height of the trapezoid first (QR):
[tex]\sqrt{37^{2} -35^{2} }[/tex] = 12
QR = 12
Area:
[tex]\frac{a+b}{2}[/tex] × h = [tex]\frac{35+41}{2}[/tex] × 12
= 456 [tex]cm^{2}[/tex]
hi I have no idea how to do this question :)
Answers
Answer:
A. 36
Step-by-step explanation:
Because the two angles at the bottom of both the triangles are congruent, the two triangles are similar. Therefore, the corresponding side lengths of the triangles must be proportional to each other
if the area of a triangle is hb/2,
(with h=length of height, b=length of base)
the height of the first triangle is:
25 = 10h/2
50 = 10h
h=5
you can write ratios representing the proportions of the two triangles:
5/x = 10/12 (with x=height of second triangle)
x=6
then find the area of the second triangle with the height (6) and base (12)
(6*12)/2 = 36
The root rafter of a house has been raised to a height of 18 yards at the ridge. Half of the length of the run measures 14 yards. Find the length of the rafter.
Answers
The length of the rafter as detailed in the question is approximately; 22.80 yards
How to use Pythagoras theorem?
The formula for Pythagoras theorem is;
a² + b² = c²
where;
a and b are adjacent and opposite sides of the triangle formed
c is the hypotenuse
Now, a rafter is a sloped member of a roof structure. Thus, if the rafter is raised to a height of 18 yeards, it means that is the vertical height of the top of the rafter to the bottom of the kingpost.
Now, if half the length run is 14 yards, it means that half of the tie beams is 14 yards. Thus, from the base of the rafter to the center of the tie beams is 14 yards. Thus, we will use Pythagoras theorem to find the length of the rafter.
c = √(14² + 18²)
c = √520
c = 22.80 yards
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Please help for 50 points with solution
Answers
Answer:
(d) 60°
Step-by-step explanation:
Theorems
Interior angles of a triangle sum to 180°Angles on a straight line sum to 180°Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
⇒ (a + 20) + (a + 10) = (a + 90)
⇒ a + 20 + a + 10 = a + 90
⇒ 2a + 30 = a + 90
⇒ 2a + 30 - a = a + 90 - a
⇒ a + 30 = 90
⇒ a + 30 - 30 = 90 - 30
⇒ a = 60
Answer:
a = 60
Step-by-step explanation:
→ Find the sum of all the angles
2a + 30 + 90 - a = 180
→ Collect the a terms
a + 120 = 180
→ Find a
a = 60
Mario is having a pizza party on Saturday night. He ordered 8 pizzas. if the average person eats 1/3 of a pizza, how many persons will 8 pizzas serve?
Answers
Answer:
24 people
Step-by-step explanation:
I pizza will feed 3 people
There are 8 pizza's
8 x 3 = 24
Which scatterplot shows no correlation?
A graph with both axes unnumbered. A scattered line increases from left to right.
A graph with both axes unnumbered. A scattered line decreases from left to right.
A graph with both axes unnumbered. A short scattered line increases from left to right.
A graph with both axes unnumbered. A line zig zags up and down the graph.
Answers
Answer:
The graph has random dots all over
Step-by-step explanation: